Two-Way Tables and Fair Games

Name: Two-Way Tables and Fair Games
Author: StemPy Lab

A made-up survey asks students two questions and puts the answers in a table.

What does the table say about one answer once you know the other?
Learn to read a conditional probability straight from a two-way table, to check whether two things are independent, and to work out the expected value of a game.
Then run the game a hundred thousand times in Python and see the average land where the rule said.

3 lessons, about 1 h 15 min3 simulations10 problems3 practice questionsPython in every lesson

Course outline (3 lessons)

Lesson 1about 25 min
Conditional probability from a two-way table
A two-way table counts people by two answers at once. Once you know one answer, you look at only one row or one column, and the share inside it is a conditional probability, written $P(A \mid B)$ . This lesson reads conditional probabilities from tables and shows why $P(A \mid B)$ and $P(B \mid A)$ are different numbers.
1 simulation1 practice question1 Python program3 problems
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Lesson 2about 25 min
Checking independence in a table
Two answers in a table are independent when the share of one answer is the same in every row or column of the other. Then every count equals row total times column total divided by the grand total. This lesson checks tables for independence and explains why a real sample is never exactly independent.
1 simulation1 practice question1 Python program3 problems1 Python lab
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Lesson 3about 25 min
Expected value and fair games
The expected value of a game is the average gain per play in the long run: each outcome times its probability, added up. A game is fair when its expected gain is zero. A casino game is built with a small negative expected gain for the player, and a simulation shows the average settling exactly there.
1 simulation1 practice question1 Python program4 problems1 Python lab1 question set1 note
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10 questions · 20 min

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